Learn English – A verb for someone who isn’t really listening

I've been asking everybody I know about a verb that has been stuck on my mind, but I can't find the right word.

I'm looking for a verb for someone who listens with reluctance. For example, I'm talking about something that happened to me, but the listener simply agrees that everything I say is true. In other words, suppose someone is busy using the computer, not knowing that they're busy, I start telling them about something that happened to me; however, they don't stop me from talking so as not to hurt my feelings, nor do they ditch me. They nod their head and say for example, "Oh" or "Really?"

I'm looking for a verb to fill the blank:

Me: telling a story

Someone: "Oh"
Me: continuing the story

Someone: "really"/"nice" / or any meaningless response.

Me: If you're busy just tell me , you don't have to __________

Or the other way around:

Someone : telling a story
Me: I'm not actually listening, I'm just __________